Decompositions by sources and by subpopulations of the pietra index: two applications to professional football teams in Italy. (English) Zbl 07706159
Summary: In this paper two innovative procedures for the decomposition of the Pietra index are proposed. The first one allows the decomposition by sources, while the second one provides the decomposition by subpopulations. As special case of the latter procedure, the “classical” decomposition in two components within and between) can be easily obtained. A remarkable feature of both the proposed procedures is that they permit the assessment of the contribution to the Pietra index at the smallest possible level: each source for the first one and each subpopulation for the second one. To highlight the usefulness of these procedures, two applications are provided regarding Italian professional football (soccer) teams.
MSC:
| 62-XX | Statistics |
References:
| [1] | Alker, H.; Russett, B., On measuring inequality, Behav. Sci., 9, 207-218 (1964) · doi:10.1002/bs.3830090302 |
| [2] | Beck, AF; Moncrief, T.; Huang, B.; Simmons, JM; Sauers, H.; Chen, C.; Kahn, RS, Inequalities in neighborhood child asthma admission rates and underlying community characteristics in one US county, J. Pediatr., 163, 2, 574-580 (2013) · doi:10.1016/j.jpeds.2013.01.064 |
| [3] | Bresciani Turroni, C., Sull’interpretazione e comparazione di seriazioni di redditi o di patrimoni, Giornale degli Economisti, 34, 13-47 (1907) |
| [4] | Castagnoli, E.; Muliere, P.; Dagum, C.; Zenga, M., A note on inequality measures and the Pigou-Dalton principle of transfers, Income and Wealth Distribution, Inequality and Poverty, 171-182 (1990), Heidelberg: Springer, Heidelberg · doi:10.1007/978-3-642-84250-4_11 |
| [5] | Dagum, C., A new approach to the decomposition of the Gini income inequality ratio, Empir. Econ., 22, 515-531 (1997) · doi:10.1007/BF01205777 |
| [6] | Davydov, Y.; Zitikis, R., An index of monotonicity and its estimation: a step beyond econometric applications of the Gini index, Metron Int. J. Stat., 63, 3, 351-372 (2005) · Zbl 1416.62178 |
| [7] | De Battisti, F.; Porro, F.; Vernizzi, A., The Gini coefficient and the case of negative values, Electron. J. Appl. Stat. Anal., 12, 85-107 (2019) |
| [8] | De Capitani, L., On the relations between variability indices-part I, Stat. Appl., 11, 1, 7-22 (2013) |
| [9] | De Capitani, L., On the relations between variability indices-part II, Stat. Appl., 11, 2, 123-132 (2013) |
| [10] | De Maio, FG, Income inequality measures, J. Epidemiol. Community Health, 61, 10, 849-852 (2007) · doi:10.1136/jech.2006.052969 |
| [11] | Eliazar, II; Sokolov, IM, Measuring statistical heterogeneity: the Pietra index, Phys. A, 389, 117-125 (2010) · doi:10.1016/j.physa.2009.08.006 |
| [12] | Frosini, BV, Approximation and decomposition of Gini, Pietra-Ricci and Theil inequality measures, Empir. Econ., 43, 175-197 (2012) · doi:10.1007/s00181-011-0464-1 |
| [13] | Gravelle, H.; Sutton, M., Trends in geographical inequalities in provision of general practitioners in England and Wales, Lancet, 352, 9144, 1910 (1998) · doi:10.1016/S0140-6736(05)60402-3 |
| [14] | Habib, EB, On the decomposition of the Schutz coefficient: an exact approach with an application, Electron. J. Appl. Stat. Anal., 5, 187-198 (2012) |
| [15] | Hasan, MU; Malik, S., Income inequality measurement in Pakistan: empirical evidence from Punjab province, Pak. J. Soc. Sci., 39, 2, 391-401 (2019) |
| [16] | Hoover, EM, The measurement of industrial localization, Rev. Econ. Stat., 18, 4, 162-171 (1936) · doi:10.2307/1927875 |
| [17] | Huang, Y.; Leung, Y., Measuring regional inequality: a comparison of coefficient of variation and Hoover concentration index, Open Geogr. J., 2, 25-34 (2009) · doi:10.2174/1874923200902010025 |
| [18] | Hustopecky, J.; Vlachy, J., Identifying a set of inequality measures for science studies, Scientometrics, 1, 1, 85-98 (1978) · doi:10.1007/BF02016841 |
| [19] | Johnston, G.; Wilkinson, D., Increasingly inequitable distribution of general practitioners in Australia, 1986-96, Aust. N. Zeal. J. Public Health, 25, 1, 66-70 (2001) · doi:10.1111/j.1467-842X.2001.tb00553.x |
| [20] | Kennedy, BP; Kawachi, I.; Prothrow-Stith, D., Income distribution and mortality: cross sectional ecological study of the Robin Hood index in the United States, Br. Med. J., 312, 1004-1007 (1996) · doi:10.1136/bmj.312.7037.1004 |
| [21] | Kennedy, BP; Kawachi, I.; Prothrow-Stith, D.; Lochner, K.; Gupta, V., Social capital, income inequality, and firearm violent crime, Soc. Sci. Med., 47, 1, 7-17 (1998) · doi:10.1016/S0277-9536(98)00097-5 |
| [22] | Khanal, B., Is community forestry decreasing the inequality among its users? Study on impact of community forestry on income distribution among different users groups in Nepal, Int. J. Soc. For., 4, 2, 139-152 (2011) |
| [23] | Khosravi Tanak, A.; Mohtashami Borzadaran, G.; Ahmadi, J., Entropy maximization under the constraints on the generalized Gini index and its application in modeling income distributions, Phys. A Stat. Mech. Appl., 438, 657-666 (2015) · doi:10.1016/j.physa.2015.06.023 |
| [24] | Koolman, X.; van Doorslaer, E., On the interpretation of a concentration index of inequality, Health Econ., 13, 649-656 (2004) · doi:10.1002/hec.884 |
| [25] | KPMG.: ‘Football clubs’ valuation: the European elite 2019. Online Report (2019) |
| [26] | Lorenz, MO, Methods of measuring the concentration of wealth, Publ. Am. Stat. Assoc., 9, 70, 209-219 (1905) |
| [27] | Manero, A., The limitations of negative incomes in the Gini coefficient decomposition by source, Appl. Econ. Lett., 24, 14, 977-981 (2017) · doi:10.1080/13504851.2016.1245828 |
| [28] | Mantzavinis, GD; Theodorakis, PN; Dimoliatis, I., Robin Hood index under discussion, Aust. N. Zeal. J. Public Health, 26, 1, 79-80 (2002) · doi:10.1111/j.1467-842X.2002.tb00277.x |
| [29] | Mobaraki, H.; Hassani, A.; Kashkalani, T.; Khalilnejad, R.; Ehsani Chimeh, E., Equality in distribution of human resources: the case of Iran’s ministry of health and medical education, Iran. J. Public Health, 42, 161-165 (2013) |
| [30] | Moothathua, TSK, On unbiased estimation of Gini index and Yntema-Pietra index of lognormal distribution and their variances, Commun. Stat. Theory Methods, 18, 2, 661-672 (1989) · Zbl 0696.62107 · doi:10.1080/03610928908829925 |
| [31] | Pasquazzi, L.; Zenga, M., Components of Gini, Bonferroni, and Zenga inequality indexes for EU income data, J. Off. Stat., 34, 1, 149-180 (2018) · doi:10.1515/jos-2018-0008 |
| [32] | Pietra, G.: Delle relazioni tra gli indici di variabilitá. Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti LXXIV(2) (1915) |
| [33] | PwC.: Accounting for typical transactions in the football industry. Online Report (2018) |
| [34] | Ray, J.; Singer, J., Measuring the concentration of power in the international system, Sociol. Methods Res., 1, 4, 403-437 (1973) · doi:10.1177/004912417300100401 |
| [35] | Ricci, U., L’ indice di variabilitá e la curva dei redditi, Giornale degli Economisti e Rivista di Statistica, 53, 177-228 (1916) |
| [36] | Rogerson, PA; Plane, DA, The Hoover index of population concentration and the demographic components of change: an article in memory of Andy Isserman, Int. Reg. Sci. Rev., 36, 1, 97-114 (2013) · doi:10.1177/0160017612440811 |
| [37] | Sarabia, JM; Chotikapanich, D., Parametric Lorenz curves: models and applications, Modeling Income Distributions and Lorenz Curves. Social Exclusion and Well-Being, 167-190 (2008), York: Springer, York · Zbl 1151.91658 · doi:10.1007/978-0-387-72796-7_9 |
| [38] | Sarabia, JM; Jorda, V., Explicit expressions of the Pietra index for the generalized function for the size distribution of income, Phys. A, 416, 582-595 (2014) · doi:10.1016/j.physa.2014.09.025 |
| [39] | Schutz, R., On the measurement of income inequality, Am. Econ. Rev., 41, 107-122 (1951) |
| [40] | Shi, L.; Macinko, J.; Starfield, B.; Wulu, J.; Regan, J.; Politzer, R., The relationship between primary care, income inequality and mortality in US states, 1980-1995, J. Am. Board Family Pract., 16, 412-422 (2003) · doi:10.3122/jabfm.16.5.412 |
| [41] | Shorrocks, AF, Inequality decomposition by factor components, Econometrica, 50, 193-211 (1982) · Zbl 0474.90032 · doi:10.2307/1912537 |
| [42] | Shorrocks, AF, Inequality decomposition by population subgroups, Econometrica, 52, 1369-1385 (1984) · Zbl 0601.90029 · doi:10.2307/1913511 |
| [43] | Shumway, J.; Otterstrom, S., Spatial patterns of migration and income change in the mountain west: the dominance of service-based, amenity-rich counties, Prof. Geogr., 53, 4, 492-502 (2001) · doi:10.1111/0033-0124.00299 |
| [44] | Theodorakis, PN; Mantzavinis, GD; Rrumbullaku, L.; Lionis, C.; Trell, E., Measuring health inequalities in Albania: a focus on the distribution of general practitioners, Hum. Resour. Health, 4, 5, 1-9 (2006) |
| [45] | Wilkinson, D.; Symon, B., Inequitable distribution of general practitioners in Australia: estimating need through the Robin Hood index, Aust. N. Zeal. J. Public Health, 24, 1, 71-75 (2000) · doi:10.1111/j.1467-842X.2000.tb00726.x |
| [46] | Zafari, B.; Ekin, T., Topic modelling for medical prescription fraud and abuse detection, J. R. Stat. Soc. Ser. C (Applied Statistics), 68, 3, 751-769 (2019) · doi:10.1111/rssc.12332 |
| [47] | Zenga, M., Decomposition by sources of the Gini, Bonferroni and Zenga inequality indexes, Stat. Appl., 11, 2, 133-161 (2013) |
| [48] | Zenga, M.; Valli, I., On the decomposition by subpopulations of the point and synthetic Bonferroni inequality measures, Stat. Appl., 14, 1, 3-28 (2016) |
| [49] | Zenga, M.; Valli, I., Joint decomposition by subpopulations and sources of the point and synthetic Bonferroni inequality measures, Stat. Appl., 15, 2, 83-120 (2017) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
